First shiny I ever found was a Zubat in Zubat Altering Cave in Emerald. Because I didn't know the cave was actually good for nothing, I had been bumping into things, messing around, pushing buttons trying to figure out the secret to it. Out pops a shiny and I think I actually DID break the game; I promptly killed it and left the cave, hoping my save would be OK.
A while later, I find a shiny Wurmple on Route 2 in RSE. Thinking the worst, I almost have my Salamence incinerate it with hyper beam, but I stop because I see it actually has a shiny animation; it can't be a bug if it is seemingly intentional. That was one lucky Wurmple.
In ORAS, hearing about how great this "Dexnav" was, I tried to chain for a shiny linoone to lead my pickup brigade. Took around ~70, but I found it. Also went for a shiny Zorua just because it's a relative's favorite Pokemon. Took a while longer, but I got it.
Other than that, I bred for a competitive Timid shiny Gastly in ORAS w/ egg moves. Of course, it ends up being 4v when coming from two 5v parents and ends up with a terrible special attack. That's one that can be redeemed by Hyper Training, at least. Additionally, I was starting a breeding project for a 5v ZardX Charmander, and of course get a shiny when changing parents for IVS. Because I checked, Dragon Dance was overwritten on one parent for Scary Face.
I ragequit that project.